T. Riste – författare

This volume contains the proceedings of a NATO Advanced study Institute held at Geilo, Norway between 2 - 12 april 1991. This institute was the eleventh in a series held biannually at Geilo on the subject of phase transitions. It was intended to capture the latest ideas on selforgan­ ized patterns and criticality. The Institute brought together many lecturers, students and active re­ searchers in the field from a wide range of NATO and non-NATO countries. The main financial support came from the NATO scientific Affairs Divi­ sion, but additional support was obtained from the Norwegian Research Council for Science and the Humanities (NAVF) and Institutt for energi­ teknikk. The organizers would like to thank all these contributors for their help in promoting an exciting and rewarding meeting, and in doing so are confident that they echo the appreciation of all the parti­ cipants. In cooperative, equilibrium systems, physical states are described by spatio-temporal correlation functions. The intimate connection between space and time correlations is especially apparent at the critical point, the second order phase transition, where the spatial range and the decay time of the correlation function both become infinite. The salient features of critical phenomena and the history of the devel­ opment of this field of science are treated in the first chapter of this book.

Recent years have seen a growing interest in and activity at the interface between physics and biology, with the realization that both subjects have a great deal to learn from and to teach to one another. A particularly promising aspect of this interface concerns the area of cooperative phenomena and phase transitions. This book addresses both the structure and motion of biological materials and the increasingly complex behaviour that arises out of interactions in large systems, giving rise to self organization, adaptation, selection and evolution: concepts of interest not only to biology and living systems but also within condensed matter physics. The approach adopted by the text is tutorial, but the book is fully up to date with the latest research. Written at a level appropriate to graduate researchers, preferably with a background either in condensed matter physics or theoretical or physically-oriented experimental biology.

This book contains the papers presented at the NATO Advanced Study Institute held at Geilo, Norway, 11th - 20th April 1975. The institute was the third in a row devoted to phase transitions. The previous two dealt with 2nd- and 1st-order transitions in equilibrium systems and the proceedings have been published.i~ In order to make an overlap wi th those institutes, the first part of this institute was devoted to 1st -or der transitions with an emphasis on the problems of metast abi l i t y and instability en­ countered i n spinodal decomposition, nucleation etc. The main topic was, however, that of non-equilibrium systems, and the present institute was to our knowledge the first one devoted to the physics of such systems. The discovery of the analogy between phase transitions in equilibrium systems and instabilities in non-equilibrium systems was first made by Rolf Landauer in 1961 and later independently by others. The analogy was first pointed out for electronic devices (tunnel diodes, Gunn oscillators, lasers, etc. ) and the treatment of hydrodynamic instabilities followed later.

This book contains the papers presented at the NATO Advanced Study Institute held at Geilo, Norway, 11th - 20th April 1975. The institute was the third in a row devoted to phase transitions. The previous two dealt with 2nd- and 1st-order transitions in equilibrium systems and the proceedings have been published.i~ In order to make an overlap wi th those institutes, the first part of this institute was devoted to 1st -or der transitions with an emphasis on the problems of metast abi l i t y and instability en­ countered i n spinodal decomposition, nucleation etc. The main topic was, however, that of non-equilibrium systems, and the present institute was to our knowledge the first one devoted to the physics of such systems. The discovery of the analogy between phase transitions in equilibrium systems and instabilities in non-equilibrium systems was first made by Rolf Landauer in 1961 and later independently by others. The analogy was first pointed out for electronic devices (tunnel diodes, Gunn oscillators, lasers, etc. ) and the treatment of hydrodynamic instabilities followed later.

This NATO Advanced Study Institute was the fourth in a series devoted to the subject of phase transitions and instabilities with particular attention to structural phase transforma~ions. Beginning wi th the first Geilo institute in 19''(1 we have seen the emphasis evolve from the simple quasiharmonic soft mode description within the Landau theory, through the unexpected spectral structure re­ presented by the "central peak" (1973), to such subjects as melting, turbulence and hydrodynamic instabilities (1975). Sophisticated theoretical techniques such as scaling laws and renormalization group theory developed over the same period have brought to this wide range of subjects a pleasing unity. These institutes have been instrumental in placing structural transformations clearly in the mainstream of statistical physics and critical phenomena. The present Geilo institute retains some of the counter cul­ tural flavour of the first one by insisting whenever possible upon peeking under the skirts of even the most successful phenomenology to catch a glimpse of the underlying microscopic processes. Of course the soft mode remains a useful concept, but the major em­ phasis of this institute is the microscopic cause of the mode softening. The discussions given here illustrate that for certain important classes of solids the cause lies in the electron phonon interaction. Three major types of structural transitions are considered. In the case of metals and semimetals, the electron phonon interaction relie6 heavily on the topology of the Fermi surface.

This NATO Advanced Study Institute was the fourth in a series devoted to the subject of phase transitions and instabilities with particular attention to structural phase transforma~ions. Beginning wi th the first Geilo institute in 19'(1 we have seen the emphasis evolve from the simple quasiharmonic soft mode description within the Landau theory, through the unexpected spectral structure re­ presented by the "central peak" (1973), to such subjects as melting, turbulence and hydrodynamic instabilities (1975). Sophisticated theoretical techniques such as scaling laws and renormalization group theory developed over the same period have brought to this wide range of subjects a pleasing unity. These institutes have been instrumental in placing structural transformations clearly in the mainstream of statistical physics and critical phenomena. The present Geilo institute retains some of the counter cul­ tural flavour of the first one by insisting whenever possible upon peeking under the skirts of even the most successful phenomenology to catch a glimpse of the underlying microscopic processes. Of course the soft mode remains a useful concept, but the major em­ phasis of this institute is the microscopic cause of the mode softening. The discussions given here illustrate that for certain important classes of solids the cause lies in the electron phonon interaction. Three major types of structural transitions are considered. In the case of metals and semimetals, the electron phonon interaction relie6 heavily on the topology of the Fermi surface.

Recent years have seen a growing interest in and activity at the interface between physics and biology, with the realization that both subjects have a great deal to learn from and to teach to one another. A particularly promising aspect of this interface concerns the area of cooperative phenomena and phase transitions. The present book addresses both the structure and motion of biological materials and the increasingly complex behaviour that arises out of interactions in large systems, giving rise to self organization, adaptation, selection and evolution: concepts of interest not only to biology and living systems but also within condensed matter physics. The approach adopted by Physics of Biomaterials: Fluctuations, Self Assembly and Evolution is tutorial, but the book is fully up to date with the latest research. Written at a level appropriate to graduate researchers, preferably with a background either in condensed matter physics or theoretical or physically-oriented experimental biology.

This book contains the papers presented at the NATO Advanced Study Institute held at Ustaoset H[cent]yfjellshotel, near Geilo, Norway, 24th April - 1st May, 1973. The members of the Programme Committee were J. D. Axe Brookhaven National Laboratory, USA J. Feder University of Oslo, Norway T. Riste Institutt for Atomenergi, Norway (Chairman) The title of the institute, "Anharmonic Lattices, Structural Transi tions and Melting", gives an idea of the programme and of the content of this book. The first part is devoted to the so- called "central mode" at 2nd order structural phase transitions, a phenomenon which was first reported in 1971 at a NATO Advanced Study Institute held at Geilo. (Several references to the pro- ceedings of that institute, entitled "Structural Phase Transitions and Soft MOdes", are found in the present volume). From 2nd order transitions the emphasis of the programme moves gradually to 1st order transitions by covering such topics as order-disorder structural transitions in simple molecular crystals and tricritical phenomena. The last part is devoted to melting, including dis- cussions on the dynamics of solids and liquids near their melting points.The lectures are divided almost equally between review talks and research reports dealing with subjects closely connected with the topics under review. With a few exceptions the lectures are printed in the sequence of presentation at the study institute. The total number of participants was limited to 71, their names are given at the end of the book.

Systems with competing energy scales are widespread and exhibit rich and subtle behaviour, although their systematic study is a relatively recent activity. This text presents lectures given at a NATO Advanced Study Institute reviewing the current knowledge and understanding of this fascinating subject, particularly with regard to phase transitions and dynamics, at an advanced tutorial level.Both general and specific aspects are considered, with competitions having several origins; differences in intrinsic interactions, interplay between intrinsic and extrinsic effects, such as geometry and disorder; irreversibility and non-equilibration. Among the specific physical application areas are supercooled liquids and glasses, high-temperature superconductors, flux or vortex pinning and motion, charge density waves, domain growth and coarsening, and electron solidification.

This volume contains the proceedings of a NATO Advanced study Institute held at Geilo, Norway between 2 - 12 april 1991. This institute was the eleventh in a series held biannually at Geilo on the subject of phase transitions. It was intended to capture the latest ideas on selforgan­ ized patterns and criticality. The Institute brought together many lecturers, students and active re­ searchers in the field from a wide range of NATO and non-NATO countries. The main financial support came from the NATO scientific Affairs Divi­ sion, but additional support was obtained from the Norwegian Research Council for Science and the Humanities (NAVF) and Institutt for energi­ teknikk. The organizers would like to thank all these contributors for their help in promoting an exciting and rewarding meeting, and in doing so are confident that they echo the appreciation of all the parti­ cipants. In cooperative, equilibrium systems, physical states are described by spatio-temporal correlation functions. The intimate connection between space and time correlations is especially apparent at the critical point, the second order phase transition, where the spatial range and the decay time of the correlation function both become infinite. The salient features of critical phenomena and the history of the devel­ opment of this field of science are treated in the first chapter of this book.

Recent years have seen a growing interest in and activity at the interface between physics and biology, with the realization that both subjects have a great deal to learn from and to teach to one another. A particularly promising aspect of this interface concerns the area of cooperative phenomena and phase transitions. The present book addresses both the structure and motion of biological materials and the increasingly complex behaviour that arises out of interactions in large systems, giving rise to self organization, adaptation, selection and evolution: concepts of interest not only to biology and living systems but also within condensed matter physics. The approach adopted by Physics of Biomaterials: Fluctuations, Self Assembly and Evolution is tutorial, but the book is fully up to date with the latest research. Written at a level appropriate to graduate researchers, preferably with a background either in condensed matter physics or theoretical or physically-oriented experimental biology.

Systems with competing energy scales are widespread and exhibit rich and subtle behaviour, although their systematic study is a relatively recent activity. This text presents lectures given at a NATO Advanced Study Institute reviewing the current knowledge and understanding of this fascinating subject, particularly with regard to phase transitions and dynamics, at an advanced tutorial level. Both general and specific aspects are considered, with competitions having several origins; differences in intrinsic interactions, interplay between intrinsic and extrinsic effects, such as geometry and disorder; irreversibility and non-equilibration. Among the specific physical application areas are supercooled liquids and glasses, high-temperature superconductors, flux or vortex pinning and motion, charge density waves, domain growth and coarsening, and electron solidification.